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Then, we propose a very simple and efficient way to implement the original filtering from its transposed version.
It is well known that the adder cost for a single-input single-output adder graph is equal to its transposed form [44].
For a differentiable function g : ℜ n → ℜ m, the Jacobian of g at x ∈ ℜ n is denoted by J g ( x ), and its transposed by ∇g(x).
Here A denotes the square matrix with the elements a i, j, ∇ x is the nabla operator and ∇ x T its transposed, i.e., ∇ x T is the row vector with the components ∂ x j.
The Sobel convolution kernel ω x and its transposed form ω y are used to obtain I x = I X, Y) ⊗ ω x , and I y = I X, Y) ⊗ ω y.
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Play your guitar in its newly transposed key.
A connection is symmetric if it coincides with its transpose.
It is the matrix Q, more precisely its transpose, which purges the vector of the unknowns from the false degrees of freedom.
The procedure described above to build the wavelet matrix ([varPsi ]) guarantees that it is orthonormal such that its matrix inverse is equal to its transpose, ([varPsi ]^{-1} = [varPsi ]^T) 2.
Fact 3: Any matrix A has the same eigenvalues as its transpose At.
The approach favors algorithms for multiplying the sensitivity matrix and its transpose with arbitrary vectors.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com